Models which simulate various aspects of the phenomenon of "bursting" in invertebrate central neurons are investigated, (bursting is the name given to the phenomenon in which a neuron generates brief "bursts" of action potentials separated by silent periods during which the cell membrane is hyperpolarized). Models have been developed for single bursting pacemaker neurons in molluscan abdominal ganglion, for crustacian cardiac pacemaker cells, and for clusters of electrotonically connected cells which display bursting when one or more of them are stimulated. Numerical solutions of the differential equations of these models are used to formulate testable hypotheses and differential predictions concerning the properties of bursting cells. Mathematical analysis is also performed in these equations. The study is especially concerned with the effects of the alkalai metal cations on the properties of these cells.